To combine like terms in the given polynomials, we simply add or subtract the coefficients of the terms with the same degree. Here's how it's done for each expression:
1. \((k^2 - 4k + 7) + (k^2 + 9k - 3)\)
Combine like terms:
- \(k^2\) terms: \(k^2 + k^2 = 2k^2\)
- \(k\) terms: \(-4k + 9k = 5k\)
- Constant terms: \(7 - 3 = 4\)
Result: \[ 2k^2 + 5k + 4 \]
2. \((w^3 - 2w^2 - 5) + (3w^2 - 11)\)
Combine like terms:
- \(w^3\) terms: \(w^3\) (only one \(w^3\) term)
- \(w^2\) terms: \(-2w^2 + 3w^2 = 1w^2\) or just \(w^2\)
- Constant terms: \(-5 - 11 = -16\)
Result: \[ w^3 + w^2 - 16 \]
3. \((9x - 5y) + (3x + 2y - 7)\)
Combine like terms:
- \(x\) terms: \(9x + 3x = 12x\)
- \(y\) terms: \(-5y + 2y = -3y\)
- Constant term: \(-7\) (only one constant term)
Result: \[ 12x - 3y - 7 \]
Final Results:
- \( 2k^2 + 5k + 4 \)
- \( w^3 + w^2 - 16 \)
- \( 12x - 3y - 7 \)
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